This work addresses the fundamental limits imposed by the MRI process on the accuracy with which vessel diameters and cross-sectional areas can be derived from time-of-flight (TOF) and phase-contrast (PC) MR source images. By means of simulations and in vitro experiments, it is demonstrated that, even in the absence of flow-related artifacts, severe inaccuracies in the determination of diameters or cross-sectional areas may occur solely because of the physical process of the MR image acquisition. Resolution and intraluminal saturation have strong effects on the vessel appearance and thus on the diameter estimation error. It is shown that low resolution leads to diameter overestimation or even underestimation and that intraluminal saturation causes severe underestimation, even for relatively low flip angles. Velocity and velocity encoding do not have a major influence on lumen appearance in PC images. Accurate diameter estimations can be attained only if lumen diameters constitute at least three pixels for both TOF and PC acquisitions, provided that intraluminal saturation is suppressed or avoided. Additionally, since the constitution of TOF and PC images is dissimilar, lumina should be analyzed differently to obtain accurate diameters and cross-sectional areas.